Solve for y 1/2(3/2y+1/3)=-1/2(y-5/2)

$\frac{1}{2} (\frac{3}{2} y + \frac{1}{3}) = - \frac{1}{2} (y - \frac{5}{2})$

Simplify $\frac{1}{2} \cdot (\frac{3}{2} y + \frac{1}{3})$ .

Start simplifying.

$0 + 0 + \frac{1}{2} \cdot (\frac{3}{2} y + \frac{1}{3}) = - \frac{1}{2} \cdot (y - \frac{5}{2})$

Simplify by adding zeros.

$\frac{1}{2} \cdot (\frac{3}{2} y + \frac{1}{3}) = - \frac{1}{2} \cdot (y - \frac{5}{2})$

Combine $\frac{3}{2}$ and $y$ .

$\frac{1}{2} \cdot (\frac{3 y}{2} + \frac{1}{3}) = - \frac{1}{2} \cdot (y - \frac{5}{2})$

Apply the distributive property.

$\frac{1}{2} \cdot \frac{3 y}{2} + \frac{1}{2} \cdot \frac{1}{3} = - \frac{1}{2} \cdot (y - \frac{5}{2})$

Multiply $\frac{1}{2} \cdot \frac{3 y}{2}$ .

Multiply $\frac{1}{2}$ by $\frac{3 y}{2}$ .

$\frac{3 y}{2 \cdot 2} + \frac{1}{2} \cdot \frac{1}{3} = - \frac{1}{2} \cdot (y - \frac{5}{2})$

Multiply $2$ by $2$ .

$\frac{3 y}{4} + \frac{1}{2} \cdot \frac{1}{3} = - \frac{1}{2} \cdot (y - \frac{5}{2})$

Multiply $\frac{1}{2} \cdot \frac{1}{3}$ .

Multiply $\frac{1}{2}$ by $\frac{1}{3}$ .

$\frac{3 y}{4} + \frac{1}{2 \cdot 3} = - \frac{1}{2} \cdot (y - \frac{5}{2})$

Multiply $2$ by $3$ .

$\frac{3 y}{4} + \frac{1}{6} = - \frac{1}{2} \cdot (y - \frac{5}{2})$

Simplify $- \frac{1}{2} \cdot (y - \frac{5}{2})$ .

Apply the distributive property.

$\frac{3 y}{4} + \frac{1}{6} = - \frac{1}{2} y - \frac{1}{2} (- \frac{5}{2})$

Combine $y$ and $\frac{1}{2}$ .

$\frac{3 y}{4} + \frac{1}{6} = - \frac{y}{2} - \frac{1}{2} (- \frac{5}{2})$

Multiply $- \frac{1}{2} (- \frac{5}{2})$ .

Multiply $- 1$ by $- 1$ .

$\frac{3 y}{4} + \frac{1}{6} = - \frac{y}{2} + 1 (\frac{1}{2}) \frac{5}{2}$

Multiply $\frac{1}{2}$ by $1$ .

$\frac{3 y}{4} + \frac{1}{6} = - \frac{y}{2} + \frac{1}{2} \cdot \frac{5}{2}$

Multiply $\frac{1}{2}$ by $\frac{5}{2}$ .

$\frac{3 y}{4} + \frac{1}{6} = - \frac{y}{2} + \frac{5}{2 \cdot 2}$

Multiply $2$ by $2$ .

$\frac{3 y}{4} + \frac{1}{6} = - \frac{y}{2} + \frac{5}{4}$

Move all terms containing $y$ to the left side of the equation.

Add $\frac{y}{2}$ to both sides of the equation.

$\frac{3 y}{4} + \frac{1}{6} + \frac{y}{2} = \frac{5}{4}$

To write $\frac{y}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3 y}{4} + \frac{y}{2} \cdot \frac{2}{2} + \frac{1}{6} = \frac{5}{4}$

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{y}{2}$ by $\frac{2}{2}$ .

$\frac{3 y}{4} + \frac{y \cdot 2}{2 \cdot 2} + \frac{1}{6} = \frac{5}{4}$

Multiply $2$ by $2$ .

$\frac{3 y}{4} + \frac{y \cdot 2}{4} + \frac{1}{6} = \frac{5}{4}$

Combine the numerators over the common denominator.

$\frac{3 y + y \cdot 2}{4} + \frac{1}{6} = \frac{5}{4}$

Add $3 y$ and $y \cdot 2$ .

Reorder $y$ and $2$ .

$\frac{3 y + 2 \cdot y}{4} + \frac{1}{6} = \frac{5}{4}$

Add $3 y$ and $2 \cdot y$ .

$\frac{5 y}{4} + \frac{1}{6} = \frac{5}{4}$

Move all terms not containing $y$ to the right side of the equation.

Subtract $\frac{1}{6}$ from both sides of the equation.

$\frac{5 y}{4} = \frac{5}{4} - \frac{1}{6}$

To write $\frac{5}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{5 y}{4} = \frac{5}{4} \cdot \frac{3}{3} - \frac{1}{6}$

To write $- \frac{1}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5 y}{4} = \frac{5}{4} \cdot \frac{3}{3} - \frac{1}{6} \cdot \frac{2}{2}$

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5}{4}$ by $\frac{3}{3}$ .

$\frac{5 y}{4} = \frac{5 \cdot 3}{4 \cdot 3} - \frac{1}{6} \cdot \frac{2}{2}$

Multiply $4$ by $3$ .

$\frac{5 y}{4} = \frac{5 \cdot 3}{12} - \frac{1}{6} \cdot \frac{2}{2}$

Multiply $\frac{1}{6}$ by $\frac{2}{2}$ .

$\frac{5 y}{4} = \frac{5 \cdot 3}{12} - \frac{2}{6 \cdot 2}$

Multiply $6$ by $2$ .

$\frac{5 y}{4} = \frac{5 \cdot 3}{12} - \frac{2}{12}$

Combine the numerators over the common denominator.

$\frac{5 y}{4} = \frac{5 \cdot 3 - 2}{12}$

Simplify the numerator.

Multiply $5$ by $3$ .

$\frac{5 y}{4} = \frac{15 - 2}{12}$

Subtract $2$ from $15$ .

$\frac{5 y}{4} = \frac{13}{12}$

Multiply both sides of the equation by $\frac{4}{5}$ .

$\frac{4}{5} \cdot \frac{5 y}{4} = \frac{4}{5} \cdot \frac{13}{12}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{4}{5} \cdot \frac{5 y}{4}$ .

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4}{5} \cdot \frac{5 y}{4} = \frac{4}{5} \cdot \frac{13}{12}$

Rewrite the expression.

$\frac{1}{5} (5 y) = \frac{4}{5} \cdot \frac{13}{12}$

Cancel the common factor of $5$ .

Factor $5$ out of $5 y$ .

$\frac{1}{5} (5 (y)) = \frac{4}{5} \cdot \frac{13}{12}$

Cancel the common factor.

$\frac{1}{5} (5 y) = \frac{4}{5} \cdot \frac{13}{12}$

Rewrite the expression.

$y = \frac{4}{5} \cdot \frac{13}{12}$

Simplify the right side.

Simplify $\frac{4}{5} \cdot \frac{13}{12}$ .

Cancel the common factor of $4$ .

Factor $4$ out of $12$ .

$y = \frac{4}{5} \cdot \frac{13}{4 (3)}$

Cancel the common factor.

$y = \frac{4}{5} \cdot \frac{13}{4 \cdot 3}$

Rewrite the expression.

$y = \frac{1}{5} \cdot \frac{13}{3}$

Multiply $\frac{1}{5}$ by $\frac{13}{3}$ .

$y = \frac{13}{5 \cdot 3}$

Multiply $5$ by $3$ .

$y = \frac{13}{15}$

The result can be shown in multiple forms.

Exact Form:

$y = \frac{13}{15}$

Decimal Form:

$y = 0.8\overline{6}$

Solve for y 1/2(3/2y+1/3)=-1/2(y-5/2)

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